Theorem rb-imdf 1515

Description: The definition of implication, in terms of \/ and -.. (Contributed by Anthony Hart, 17-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
rb-imdf	|- -. (-. (-. (ph -> ps) \/ (-. ph \/ ps)) \/ -. (-. (-. ph \/ ps) \/ (ph -> ps)))

Proof of Theorem rb-imdf

Step	Hyp	Ref	Expression
1		imor 401	. 2 |- ((ph -> ps) <-> (-. ph \/ ps))
2		rb-bijust 1514	. 2 |- (((ph -> ps) <-> (-. ph \/ ps)) <-> -. (-. (-. (ph -> ps) \/ (-. ph \/ ps)) \/ -. (-. (-. ph \/ ps) \/ (ph -> ps))))
3	1, 2	mpbi 199	1 |- -. (-. (-. (ph -> ps) \/ (-. ph \/ ps)) \/ -. (-. (-. ph \/ ps) \/ (ph -> ps)))

Syntax hints:  -. wn 3   -> wi 4   <-> wb 176   \/ wo 357

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-or 359

This theorem is referenced by:  re1axmp  1529  re2luk1  1530  re2luk2  1531  re2luk3  1532